Pre-Algebra Examples

$y - 8 = \frac{1}{4} \cdot (x - (- 5))$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $4$ .

$4 (y - 8) = 4 (\frac{1}{4} \cdot (x - (- 5)))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (y - 8)$ .

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Step 3.1.1

Apply the distributive property.

$4 y + 4 \cdot - 8 = 4 (\frac{1}{4} \cdot (x - (- 5)))$

Step 3.1.2

Multiply $4$ by $- 8$ .

$4 y - 32 = 4 (\frac{1}{4} \cdot (x - (- 5)))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $4 (\frac{1}{4} \cdot (x - (- 5)))$ .

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Step 4.1.1

Multiply $- 1$ by $- 5$ .

$4 y - 32 = 4 (\frac{1}{4} \cdot (x + 5))$

Step 4.1.2

Apply the distributive property.

$4 y - 32 = 4 (\frac{1}{4} x + \frac{1}{4} \cdot 5)$

Step 4.1.3

Combine $\frac{1}{4}$ and $x$ .

$4 y - 32 = 4 (\frac{x}{4} + \frac{1}{4} \cdot 5)$

Step 4.1.4

Combine $\frac{1}{4}$ and $5$ .

$4 y - 32 = 4 (\frac{x}{4} + \frac{5}{4})$

Step 4.1.5

Apply the distributive property.

$4 y - 32 = 4 \frac{x}{4} + 4 (\frac{5}{4})$

Step 4.1.6

Cancel the common factor of $4$ .

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Step 4.1.6.1

Cancel the common factor.

$4 y - 32 = 4 \frac{x}{4} + 4 (\frac{5}{4})$

Step 4.1.6.2

Rewrite the expression.

$4 y - 32 = x + 4 (\frac{5}{4})$

Step 4.1.7

Cancel the common factor of $4$ .

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Step 4.1.7.1

Cancel the common factor.

$4 y - 32 = x + 4 (\frac{5}{4})$

Step 4.1.7.2

Rewrite the expression.

$4 y - 32 = x + 5$

Step 5

Rewrite the equation.

$x + 5 = 4 y - 32$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Subtract $4 y$ from both sides of the equation.

$x + 5 - 4 y = - 32$

Step 6.2

Move $5$ .

$x - 4 y + 5 = - 32$

Step 7

Move all terms not containing a variable to the right side of the equation.

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Step 7.1

Subtract $5$ from both sides of the equation.

$x - 4 y = - 32 - 5$

Step 7.2

Subtract $5$ from $- 32$ .

$x - 4 y = - 37$

Step 8